Ryan, who was in Chicago Monday to discuss his proposal to cut the federal deficit, told one prospective candidate in Wisconsin he was "leaning heavily against a run," sources familiar with the matter said.

According to another source, Ryan, the House Budget Committee chairman, said he was "95 percent sure" he would not enter the race for the open seat.

Kohl announced Friday that he would not seek re-election in 2012, saying he believed it was better to leave a job too early than too late. Kohl, Wisconsin's 76-year-old senior senator, has served in the Senate since being elected in 1988 and has won re-election by comfortable margins three times.

On Sunday, Ryan said he would make his decision public this week.

The announcement could come as soon as Tuesday or Wednesday, Politico said, so other prospective candidates could begin organizing their campaigns.

A Ryan spokesperson did not immediately return an inquiry seeking comment.